Friday, May 9, 2014

Spinning The Unit Circle (Evaluating Trig Functions )

If you’ve ever taken a ferris wheel ride then you know about periodic motion, you go up and down over and over again.  The height of the seat is a periodic function of time; it rises and falls in a smooth, repeating manner.   Trigonometric functions can be defined in terms of the unit circle, the circle of radius one centered at the origin.  Sine and cosine are periodic functions with period 2π.  For angles greater than 2π or less than −2π, simply continue to rotate around the circle, just like the ferris wheel.

Evaluating trigonometric functions is all about knowing the unit circle (It is strongly recommended to memorize the trivial angles).

Let’s see how it works, here’s an example using a simple manipulation (click here):

Here’s an example using the periodic property (click here):

Here’s an example using trigonometric identity (click here):

Evaluating trigonometric equations might be somewhat tricky at first, but with practice you will use the same techniques over and over again…



  1. what does this mean erf mean in your integration calculator answers? Please email answer or post it here

    1. Hi Titus,

      It refers so the error function:

      Hope this helps,


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  3. It's nice to read about this technique. I will try it out later.

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